Kirchhoff migration in practice

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

In this and the following three sections, the parameters that affect performance of Kirchhoff summation, finite-difference, and f − k migration methods are discussed. In Kirchhoff migration, the important parameters are the aperture width used in summation and the maximum dip to migrate. In finite-difference and phase-shift migrations, the depth step size needs to be selected properly. The stretch factor is important in Stolt migration. The responses of these methods to velocity errors also are examined. All practical aspects are discussed using synthetic models of two zero-offset sections — a model of dipping-events and a model of a diffraction hyperbola. Real data examples also are used to evaluate the choice of optimum parameters.

Figure 4.2-1  Migration can be confined to a range of dips present on a seismic section. The impulse response for the dip-limited migration operator is a truncated semicircle. Dip angle θ is measured from the vertical axis.

In Kirchhoff migration in practice, finite-difference migration in practice, frequency-space migration in practice, and frequency-wavenumber migration in practice, migration results of different algorithms using various parameters are compared with a desired migration. In all cases, this desired migration was obtained using the phase-shift method with appropriate parameters and velocities. This does not imply that the phase-shift method always provides a desirable output; it only means that the data examples in this section were chosen so that the phase-shift algorithm is appropriate. The choice of the phase-shift method was a compromise; it handles dips of up to 90 degrees and velocities that can only vary vertically.

Before a migration algorithm is used on field data, its impulse response must be tested. A band-limited impulse response is generated by using an input that contains an isolated wavelet on one trace only To also limit the spatial bandwidth, this trace is replicated on either side with the wavelet amplitude halved. The ideal migration algorithm should produce an impulse response that has the shape of a semicircle. Kirchhoff migration produces the section shown in Figure 4.2-1d. The impulse response indicates that Kirchhoff migration can accurately handle dips up to 90 degrees. The dip on a migration impulse response is measured as the angle θ between the vertical and a specified radial direction. Note that migration can be limited to smaller dips (Figure 4.2-1).

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